
where \(\Phi _{\mathrm {I},\mathrm {S},\mathrm {R}}\) , \(\Phi _{\mathrm {I},\mathrm {R},\mathrm {D}}\)  \(\in \)  \(\mathcal {P}_M\) , \((a)\)  is because the links from S to R and R to D are symmetric and thus \(r^{\rm (R)}_{\mathrm {S,R}}\)  \(=\)  \(r^{\rm (R)}_{\mathrm {R,D}}\)  by properly designing the IRS passive beamforming (shown next),
and the factor \(\frac{1}{2}\)  is due to the fact that data is transmitted from S to D over two equal time slots.
To maximize \(r^{\rm (R)}_{\mathrm {S,R}}\)  in (REF ), it can be shown that the main diagonal of the optimal IRS passive beamforming is [1]}
